Non-linear Cyclic Codes that Attain the Gilbert-Varshamov Bound

We prove that there exist non-linear binary cyclic codes that attain the Gilbert-Varshamov bound

Application of the gradient method to Hartree-Fock-Bogoliubov theory

A computer code is presented for solving the equations of Hartree-Fock-Bogoliubov (HFB) theory by the gradient method, motivated by the need for efficient and robust codes to calculate the configurations required by extensions of HFB such as the generator coordinate method. The code is organized with a separation between the parts that are specific to the details of the Hamiltonian and the parts that are generic to the gradient method. This permits total flexibility in choosing the symmetries to be imposed on the HFB solutions. The code solves for both even and odd particle number ground states, the choice determined by the input data stream. Application is made to the nuclei in the $sd$-shell using the USDB shell-model Hamiltonian.Comment: 20 pages, 5 figures, 3 table

Sparse multivariate polynomial interpolation in the basis of Schubert polynomials

Schubert polynomials were discovered by A. Lascoux and M. Sch\"utzenberger in the study of cohomology rings of flag manifolds in 1980's. These polynomials generalize Schur polynomials, and form a linear basis of multivariate polynomials. In 2003, Lenart and Sottile introduced skew Schubert polynomials, which generalize skew Schur polynomials, and expand in the Schubert basis with the generalized Littlewood-Richardson coefficients. In this paper we initiate the study of these two families of polynomials from the perspective of computational complexity theory. We first observe that skew Schubert polynomials, and therefore Schubert polynomials, are in \CountP (when evaluating on non-negative integral inputs) and \VNP. Our main result is a deterministic algorithm that computes the expansion of a polynomial $f$ of degree $d$ in $\Z[x_1, \dots, x_n]$ in the basis of Schubert polynomials, assuming an oracle computing Schubert polynomials. This algorithm runs in time polynomial in $n$, $d$, and the bit size of the expansion. This generalizes, and derandomizes, the sparse interpolation algorithm of symmetric polynomials in the Schur basis by Barvinok and Fomin (Advances in Applied Mathematics, 18(3):271--285). In fact, our interpolation algorithm is general enough to accommodate any linear basis satisfying certain natural properties. Applications of the above results include a new algorithm that computes the generalized Littlewood-Richardson coefficients.Comment: 20 pages; some typos correcte

The digital data processing concepts of the LOFT mission

The Large Observatory for X-ray Timing (LOFT) is one of the five mission candidates that were considered by ESA for an M3 mission (with a launch opportunity in 2022 - 2024). LOFT features two instruments: the Large Area Detector (LAD) and the Wide Field Monitor (WFM). The LAD is a 10 m 2 -class instrument with approximately 15 times the collecting area of the largest timing mission so far (RXTE) for the first time combined with CCD-class spectral resolution. The WFM will continuously monitor the sky and recognise changes in source states, detect transient and bursting phenomena and will allow the mission to respond to this. Observing the brightest X-ray sources with the effective area of the LAD leads to enormous data rates that need to be processed on several levels, filtered and compressed in real-time already on board. The WFM data processing on the other hand puts rather low constraints on the data rate but requires algorithms to find the photon interaction location on the detector and then to deconvolve the detector image in order to obtain the sky coordinates of observed transient sources. In the following, we want to give an overview of the data handling concepts that were developed during the study phase.Comment: Proc. SPIE 9144, Space Telescopes and Instrumentation 2014: Ultraviolet to Gamma Ray, 91446

Aerothermal modeling. Executive summary

One of the significant ways in which the performance level of aircraft turbine engines has been improved is by the use of advanced materials and cooling concepts that allow a significant increase in turbine inlet temperature level, with attendant thermodynamic cycle benefits. Further cycle improvements have been achieved with higher pressure ratio compressors. The higher turbine inlet temperatures and compressor pressure ratios with corresponding higher temperature cooling air has created a very hostile environment for the hot section components. To provide the technology needed to reduce the hot section maintenance costs, NASA has initiated the Hot Section Technology (HOST) program. One key element of this overall program is the Aerothermal Modeling Program. The overall objective of his program is to evolve and validate improved analysis methods for use in the design of aircraft turbine engine combustors. The use of such combustor analysis capabilities can be expected to provide significant improvement in the life and durability characteristics of both combustor and turbine components

Basic Module Theory over Non-Commutative Rings with Computational Aspects of Operator Algebras

The present text surveys some relevant situations and results where basic Module Theory interacts with computational aspects of operator algebras. We tried to keep a balance between constructive and algebraic aspects.Comment: To appear in the Proceedings of the AADIOS 2012 conference, to be published in Lecture Notes in Computer Scienc

Row Reduction Applied to Decoding of Rank Metric and Subspace Codes

We show that decoding of $\ell$-Interleaved Gabidulin codes, as well as list-$\ell$ decoding of Mahdavifar--Vardy codes can be performed by row reducing skew polynomial matrices. Inspired by row reduction of \F[x] matrices, we develop a general and flexible approach of transforming matrices over skew polynomial rings into a certain reduced form. We apply this to solve generalised shift register problems over skew polynomial rings which occur in decoding $\ell$-Interleaved Gabidulin codes. We obtain an algorithm with complexity $O(\ell \mu^2)$ where $\mu$ measures the size of the input problem and is proportional to the code length $n$ in the case of decoding. Further, we show how to perform the interpolation step of list-$\ell$-decoding Mahdavifar--Vardy codes in complexity $O(\ell n^2)$, where $n$ is the number of interpolation constraints.Comment: Accepted for Designs, Codes and Cryptograph